Schools are to be handed almost £400m more as part of a government attempt to make funding fairer, but headteachers have warned that increasing costs mean many are unlikely to be better off.

In a written statement, schools minister David Laws said £390m is to be spent on increasing the budgets of local areas that previously received low funding.

He insisted that no other local council's per-pupil funding will be reduced from its current level.

Laws said: "This £390m increase – £40m more than was announced in March – is the biggest step toward fairer schools funding in a decade, and will go a long way to removing the historical unfairness of the funding system.

"Crucially, we have ensured no local authority will see a reduction in its budget, while 69 local authorities will get a cash boost.

"This increase in funding will make a real difference on the ground in the least fairly funded local areas, without creating instability, uncertainty or cuts in any areas."

Ministers had announced proposals earlier this year to tackle England's "unfair and complicated" system for allocating school funding, claiming they would set minimum funding levels and hand an extra £350m to schools in the least fairly funded areas.

As an example, Laws said that Cambridgeshire, which was the lowest funded area in 2014/15, will now get an extra £311 per pupil, whilst Northumberland will get an extra £307 and Croydon £278 more for each student.

But he added: "This good news is completely overshadowed by the reality that all schools and colleges are facing huge holes in their budgets caused by pension contribution rises and other increasing costs.

"This real terms reduction in funding will lead to larger class sizes and fewer course options as schools are no longer afford to run subjects that do not recruit well. We want to see the increase in pension contributions fully funded so that children's education is not compromised.

"The new minimum-per-pupil level only means that those schools will be hit less hard than other schools that have historically been better funded. At best, schools in low funded areas will be no worse off and schools in better funded areas will see a real term decrease in their budget."

Russell Hobby, general secretary of the National Association of Head Teachers (NAHT), said: "This focused funding, first proposed in March, is welcome and necessary. It is good to see that the 60 local areas deemed the least fairly funded will benefit.

"There is growing evidence from Ofsted, the Sutton Trust and others about the effect of clusters of deprivation and these are not always where you might expect."

He added: "However, this extra money must be seen in the context of on-going austerity for both schools and local authorities in real terms. This is at a time when pupil numbers are rising, there are questions about a sufficient supply of teachers and local authority support is being cut.

"Given these challenges this funding may not be enough for children in those areas, let alone the rest of the country."